Another error: Suou is a man, not a girl. He may look feminine to some extent, but he is male for sure. In the final page, Akira calls him "Suou-kun" too
The idea among the classes is that "Colors" is the main "national" party, one that receives support from everyone pretty much
Among the main members of Colors, each one represents a color (Leader is Red, there is Blue, and so on).
The Golden Orchid Clan would be associated with one of these colors, so it's a 2nd level party.
Soreil is a 3rd level, as in, they are related to the Golden Orchid Clan, but not directly with Colors, but you could argue there is a connection.
However, they are not the only parties related to Colors, there are many 2nd level parties related to Colors, and there are even more 3rd level parties that are related to tehse 2nd level ones.